A class of nonconforming quadrilateral membrane elements, introduced by Sander and Beckers, is discussed in all details. It is proved that two elements that do not pass the patch test may still yield convergence under a suitable condition on mesh subdivisions, whereas one such element is found to be divergent for all mesh subdivisions. All other finite elements in this class that pass the patch...

Finite element formulations based on stabilized bilinear and linear equal-order-interpolation velocity-pressure elements are presented for computation of steady and unsteady incompressible flows. The stabilization procedure involves a slightly modified Galerkin/least-squares formulation of the steady-state equations. The pressure field is interpolated by continuous functions for both the quadri...

Generally, the finite element method is a powerful procedure for analysis of tall buildings. Yet, it should be noted that there are some problems in the application of many finite elements to the analysis of tall building structures. The presence of artificial flexure and parasitic shear effects in many lower order plane stress and membrane elements, cause the numerical procedure to converge in...

The work focuses on the development of a 2D quadrilateral element based Spectral Difference solver for viscous flow calculations, and the application of the p-multigrid method and implicit time-stepping to accelerate convergence. This paper extends the previous work by Liang et al (2009) on the p-multigrid method for 2D inviscid compressible flow, to viscous flows. The high-order spectral diffe...

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence....

Conformal refinement using a shrink and connect strategy known as pillowing or buffer insertion contracts contiguous elements of an all-quadrilateral or an all-hexahedral mesh and reconnects them to locally increase vertex density. Using layers as shrink sets, the present method anisotropically refines an initial mesh to match a prescribed size map expressed as a metric field. An anisotropic sm...

This paper describes and demonstrates a process for adaptive refinement of quadrilateral curved shell meshes using error estimates from MSC.Nastran. The meshes have been generated originally using Unigraphics'(UG) Scenario application. Although refinement procedures for finite element meshes have been in use for many years, automated procedures have most generally been developed for triangular ...

One approach to achieving correct finite element assembly is to ensure that the local orientation of facets relative to each cell in the mesh is consistent with the global orientation of that facet. Rognes et al. have shown how to achieve this for any mesh composed of simplex elements, and deal.II contains a serial algorithm to construct a consistent orientation of any quadrilateral mesh of an ...

Surface mesh quality plays a very important role in the solution accuracy and in the quality of the ensuing volumetric mesh. Amongst the techniques available, optimization based methods are commonly used for mesh quality improvement. Optimization methods for volumetric and planar surface mesh quality improvement are very well researched. However, this is not true for non-planar meshes. In this ...

The cornerstone of nodal spectral element methods is the co-location of the interpolation and integration points, yielding a diagonal mass matrix that is efficient for time-integration methods. On quadrilateral elements Legendre-Gauss-Lobatto points are both good interpolation and integration points but on triangles analogous points have not yet been found. In this paper we use a promising set ...